Elman neural network assisting tight-integrated navigation method without GNSS signals

ABSTRACT

The disclosure relates to a tight-integrated navigation method assisted by Elman neural network when GNSS signals are blocked based on the tight-integrated navigation system model of the INS and GNSS. The dynamic Elman neural network prediction model is used to train the inertial navigation error model and the GNSS compensation model, so as to solve the problem of tight-integrated navigation when the GNSS signals are blocked. When the GNSS signals are blocked, the trained neural network is used to predict the output error of GNSS and compensate the output of inertial navigation, so that the error will not diverge sharply, and the system can continue to work in the integrated navigation mode. The low-cost tight-integrated navigation module is used, and the collected information is preprocessed to form the sample data for training the neural network to train the Elman neural network model.

CROSS-REFERENCE TO RELATED PATENT APPLICATION

This application claims priority to and the benefit of 201910915008.3,filed Sep. 26, 2019. The entire disclosure of the above-identifiedapplication is incorporated herein by reference.

FIELD

This disclosure relates to a tight-integrated navigation method, andmore specifically, to a tight-integrated navigation method assisted byan Elman neural network when GNSS signals are blocked.

BACKGROUND

The inertial navigation system can provide navigation informationcomprehensively and autonomously, and the errors of the inertialnavigation system will be accumulated gradually when the inertialnavigation system is low-cost. Although GNSS has a wide positioningrange and a high accuracy, the GNSS signals are easy to be blocked andinterfered. Therefore, the inertial navigation and GNSS can becomplemented with each other, and the tight integration of inertialnavigation and GNSS can make full use of these two systems. The tightintegration can also improve the accuracy and reliability of thenavigation system. However, for the tight-integrated navigation system,when satellite signals are unavailable for a short period of time due tothe blocking or interference, the tight-integrated navigation systemworks in inertial navigation mode only, and at this time the navigationaccuracy depends on the accuracy of the inertial navigation device orthe accuracy of the tight-integrated navigation at the previous momentwhen the GNSS is unavailable. Since the errors of the low-cost inertialnavigation systems are accumulated gradually and cannot be corrected,the navigation accuracy will be decreased rapidly, and even that thenavigation system will not be used.

The reason, why the accuracy of the tight-integrated navigation systemis decreased rapidly without the GNSS signals, is that the priorinertial navigation error model is difficult to satisfy the actualsituation in lack of external observations. If an accurate inertialnavigation error model is obtained at the current time, even when theGNSS signals are blocked, this accurate error model can also be used tocalculate the error of the inertial navigation system, and finally theerror of the inertial navigation can be compensated. Neural networkshave good nonlinear mapping capabilities and can simulate the input andoutput of actual models. Traditional neural networks, such as BP neuralnetwork, multilayer perceptron neural network, radial basis functionneural network and the like, can be used to derive the inertialnavigation error model, but these neural networks are static networks,and are not easy to accurately describe the dynamic characteristics ofnonlinear systems.

SUMMARY

Embodiments of the present disclosure provide a tight-integratednavigation method assisted by an Elman neural network when GNSS signalsare blocked, which can accurately describe the dynamic characteristicsof nonlinear systems. The Elman neural network is a typical multilayerdynamic recurrent neural network, which can predict the inertialnavigation error signal when the GNSS signals are temporarily blocked,and compensate and correct the output of the inertial navigation by thepredicted data, so that the integrated navigation system can continue toprovide navigation data when the GNSS signals are momentarilyunavailable.

An Elman neural network assisting tight-integrated navigation methodwithout GNSS signals, comprising:

Step 1: establishing an Elman neural network model and selecting ahidden layer transfer function of the Elman neural network,

Step 2: designing an Elman learning algorithm,

Step 3: establishing a tight-integrated Kalman filter mathematicalmodel,

Step 4: when the GNSS signals are available, the neural network works ina training mode, a three-dimensional position information output by aninertial navigation system is used as input samples for training theneural network designed in the step 2; a compensation value of aninertial navigation error output after a fusion of the Kalman filterestablished in step 3 is used as expected output samples for trainingthe network, and the input samples and the expected output samples arebrought into the Elman neural network established in the step 2 fortraining the Elman neural network; when errors between actual outputs ofthe Elman neural network and the expected output samples are more than apredetermined threshold, an updated value of a network weight isobtained by cyclically using the Elman neural network algorithm designedin step 2 until the errors between the actual outputs of the network andthe expected outputs are less than the predetermined threshold, and

Step 5: when the GNSS signals are blocked, the neural network works in aprediction mode; a navigation position information output by theinertial navigation system is used as the input of the network trainedby the step 4, an error of the inertial navigation system is predictedby the neural network model trained by the step 4, and a correctednavigation information is obtained by correcting the navigation outputof the inertial navigation system by the error predicted by the neuralnetwork model.

The present disclosure further comprising,

The Elman neural network comprises an input layer, a hidden layer, aconnection layer and an output layer, the mathematical model of theElman neural network is expressed as follows:

xh(k)=f(W1P(k)+W3×(k));

xc(k)=αxh(k−1);

y(k)=g(W2×(k));

Wherein, P(k) represents an input vector of the Elman neural network attime k, xh(k) represents an output vector of the hidden layer neuron attime k, x(k) represents an input vector of the Elman neural networkderived from the output of the hidden layer at time k, xc(k) representsan output vector of the connection layer at time k, y(k) represents theoutput vector of the entire network output layer at time k, W1, W2 andW3 are respectively connection weight matrixes between the input layerand the hidden layer, between the hidden layer and the output layer, andbetween the connection layer and the hidden layer, f(⋅) and g(⋅) arerespectively transfer functions of the hidden layer and the outputlayer, and α is a connection feedback gain factor.

An S-tangent function is selected as the transfer function of the hiddenlayer of Elman neural network.

The step 2 comprises,

A calculation process of the Elman neural network is divided to comprisea forward propagation of a working signal and a backward propagation ofthe error; the calculation of the forward propagation of the workingsignal is in consistent with the mathematical model of the Elman neuralnetwork, and the signal y(k) of the network output is calculated;

The back propagation of the error is as follows: that the actual outputof the network is y(k) at time k is assumed, and the expected outputresponse of the network is yd(k), then the error of the network is asfollows:

E _(k)=½(y _(d)(k))²

Partial derivatives of the error function with respect to the connectionweights between different layers are obtained, respectively; the partialderivative of the error function Ek with respect to the connectionweight matrix W2 from the hidden layer to the output layer is obtainedas follows:

$\frac{\partial E}{\partial w_{ij}^{2}} = {{{- \left( {{y_{d,i}(k)} - {y(k)}} \right)}\frac{\partial{y_{i}(k)}}{\partial w_{ij}^{2}}} = {{- \left( {{y_{d,i}(k)} - {y(k)}} \right)}{g(\bullet)}{x_{j}(k)}}}$

Wherein, i represents an i-th hidden layer neuron, which is the i-th rowof the weight matrix W2, and j represents a j-th output layer neuron,which is the j-th column of the weight matrix W2;

Assuming δ_(i) ⁰=(y _(d,i)(k)−y(k))g(∩), then:

$\frac{\partial E}{\partial w_{ij}^{2}} = {{- \delta_{i}^{0}}{x_{j}(k)}}$

The partial derivative of Ek with respect to the connection weightmatrix W1 from the input layer to the hidden layer is obtained asfollows:

$\frac{\partial E}{\partial w_{ij}^{1}} = {{\frac{\partial E}{\partial{x_{j}(k)}}\frac{\partial{x_{j}(k)}}{\partial w_{ij}^{1}}} = {\sum{\left( {{- \delta_{i}^{0}}w_{ij}^{2}} \right){f_{j}^{\prime}(\bullet)}{P\left( {k - 1} \right)}}}}$

Assuming

${\delta_{j}^{h} = {\sum\limits_{i = 1}^{m}{\left( {{- \delta_{i}^{0}}w_{ij}^{2}} \right){f_{j}^{\prime}(\bullet)}}}},$

then:

$\frac{\partial E}{\partial w_{ij}^{1}} = {{- \delta_{i}^{h}}{P\left( {k - 1} \right)}}$

The partial derivative of Ek with respect to the connection weightmatrix W3 from the connection layer to the hidden layer is obtained asfollows:

$\frac{\partial E}{\partial w_{ij}^{3}} = {{\sum{\left( {{- \delta_{i}^{0}}w_{ij}^{2}} \right)\frac{\partial{x_{j}(k)}}{\partial w_{ij}^{3}}}} = {{f_{j}^{\prime}{x_{c,l}(k)}} = {{{f_{j}^{\prime}(\bullet)}{x_{i}\left( {k - 1} \right)}} + {\alpha \; {f_{i}^{\prime}(\bullet)}{x_{c,l}(k)}}}}}$

Wherein, 1 is the 1-th neuron of the connection layer;

Using

${{\Delta \; w} = {- \frac{\partial E}{\partial w}}},$

updated values for each weight may be obtained as follows:

Δ w_(ij)² = η δ_(i)⁰x_(j)(k) Δ w_(j)¹ = η δ_(i)P(k − 1)${\Delta \; w_{ij}^{3}} = {\eta {\sum{\left( {\delta_{i}^{0}w_{ij}^{2}} \right)\frac{\partial{x_{j}(k)}}{\partial w_{jl}^{3}}\delta_{i}^{0}{x_{j}(k)}}}}$

Wherein,

δ_(i) ⁰=(y _(d,i)(k)−y(k))g _(i)(⋅)

δ_(j) ^(h)=Σ(δ_(i) ⁰ w _(ij) ²)f′ _(j)(⋅)

The step 3 comprises,

15-dimensional system state variables selected are as follows:

X=[δposδVδφε∇b_(clk)d_(clk)]

Wherein, δpos is three position errors of the ECEF coordinate system, δVis a velocity error in the ENU coordinate system, δ_(φ) is three postureerrors of the inertial navigation system, ε is three posture angleerrors, ∇ is acceleration zero-biases in three directions, b_(clk) is aclock error, and d_(clk) is a clock drift;

An external observation is obtained by the difference Z between thepseudo-range information and pseudo-range rate information obtained bythe inertial navigation system and the measurement information of thepseudo-range and pseudo-range rate of each GNSS satellite, a systemmeasurement equation is as follows:

$Z = {\begin{bmatrix}Z_{\rho} \\Z_{\overset{.}{\rho}}\end{bmatrix} = {{HX} - V}}$

Wherein, H is an observation matrix, V is an observation noise, ρ is apseudo-range, and {dot over (P)} is a pseudo-range rate;

A filtering calculation is performed by the EKF for the integratednavigation, the detailed filtering calculation is as follows:

one-step prediction status:

Xk,k−1=φk,k−1Xk−1

A status estimation:

Xk=Xk,k−1+Kk[Zk−hk(Xk,k−1)]

A one-step prediction error variance matrix:

P _(k,k . . . 1)=ϕ_(k,k . . . 1) P _(k . . . 1)ϕ_(k,k . . . 1) ^(T) +Q_(k . . . 1)

A filter gain matrix:

K _(k) =P _(k,k . . . 1) H _(k) ^(T)(H _(K) P _(k,k . . . 1) H _(k) ^(T)+R _(K))⁻¹

An estimation error variance matrix:

Pk=(I−KkHk)Pk,k−1

Wherein, Φ is an error status transfer matrix, K is a Kalman gainmatrix, P is an error covariance matrix, and R is a noise covariancematrix;

The corrected position information X in three directions is calculatedby the aforementioned Kalman filter, and the difference between thepositions before and after the correction is brought into theestablished Elman neural network as an output of neural network duringthe neural network training.

The step 4 comprises during network training, the number of inputneurons and output neurons of the network is the number of positionparameters in three directions in the ECEF coordinate system, m is 3;the number I of neurons in the hidden layer is 3; the input of thenetwork is the position informations {circumflex over (x)}_(k) output bythe inertial navigation of the integrated navigation system, the targetoutput of the network is the compensation inertial navigation positionΔE after filtering of the integrated system; the input samples andoutput samples are brought into the y(k) and yd (k) of the Elman neuralnetwork established in the step 2 to train the neural network, and theoutput x _(k) corrected by neural network is obtained after the trainingis completed,

Wherein, ΔE=X _(k)−{circumflex over (X)}_(k)

The data of ΔE are saved in the Elman neural network model, and theerror of the inertial navigation is corrected by retrieving the errordata ΔE at the corresponding sampling time;

The position x _(k) in the three directions in the ECEF coordinatesystem is compensated in order to make a prediction,

X _(k)={circumflex over (X)}_(k)+ΔE

The status prediction estimation in the integrated navigation iscorrected in real time according to the trained network, and whencorrecting, the status variable {circumflex over (X)}_(k) of the EKFfilter of the integrated system is replaced by the x _(K).

The advantages of the aspects of embodiments of the present disclosurelie in that: the Elman neural network is a typical multilayer dynamicrecurrent neural network, which can predict the inertial navigationerror signal when the GNSS signals are temporarily blocked, andcompensate and correct the output of the inertial navigation by thepredicted data, so that the integrated navigation system can continue toprovide navigation data when the GNSS signals are momentarilyunavailable.

The dynamic Elman neural network prediction model is used to train theinertial navigation error model and the GNSS compensation model, so asto solve the problem of tight-integrated navigation when the GNSSsignals are blocked. When the GNSS signals are blocked, the trainedneural network is used to predict the output error of GNSS andcompensate the output of inertial navigation, so that the error will notdiverge sharply, and the system can continue to work in the integratednavigation mode. The low-cost tight-integrated navigation module isused, and the collected information is preprocessed to form the sampledata for training the neural network to train the Elman neural networkmodel. In the present disclosure, the output error of GNSS can bepredicted when the GNSS signals are blocked for 100s, so that thenavigation system can still work in tight-integrated navigation mode.

An Elman neural network assisting tight-integrated navigation system,comprising: a GNSS receiver for receiving GNSS signals, an INS receiverfor receiving INS signals, a Kalman filter for executing a filteringprocess of received signals, and a processor operable to establish anElman neural network model and selecting a hidden layer transferfunction of the Elman neural network, design an Elman learningalgorithm, and establish a tight-integrated Kalman filter mathematicalmodel, wherein, when the GNSS signals are available, the Elman neuralnetwork works in a training mode, a three-dimensional positioninformation outputted by the INS receiver is used as input samples fortraining the Elman neural network designed by the processer; acompensation value of an inertial navigation error output after a fusionof the Kalman filter is used as expected output samples for training theElman neural network, and the input samples and the expected outputsamples are brought into the Elman neural network established fortraining the Elman neural network; when errors between actual outputs ofthe Elman neural network and the expected output samples are more than apredetermined threshold, an updated value of a network weight isobtained by cyclically using the Elman neural network until the errorsbetween the actual outputs of the Elman neural and the expected outputsare less than the predetermined threshold, and when the GNSS signals areblocked, the Elman neural network works in a prediction mode; anavigation position information output by the INS receiver is used asthe input of the trained neural network, an error of the inertialnavigation system is predicted by the trained neural network, and acorrected navigation information is obtained by correcting thenavigation output of the INS receiver by the error predicted by theElman neural network.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a topology diagram of an Elman neural network.

FIG. 2 is an S-type logarithmic function.

FIG. 3 is an S-type tangent function.

FIG. 4 is a linear function.

FIG. 5 is a schematic view of training Elman neural network.

FIG. 6 is a schematic view of prediction process of Elman neuralnetwork.

FIG. 7 is a graph of X-axis position error before GNSS signals areblocked.

FIG. 8 is a graph of Y-axis position error before GNSS signals areblocked.

FIG. 9 is a graph of Z-axis position error before GNSS signals areblocked.

FIG. 10 is a graph of X-axis position error after GNSS signals areblocked.

FIG. 11 is a graph of Y-axis position error after GNSS signals areblocked.

FIG. 12 is a graph of Z-axis position error after GNSS signals areblocked.

FIG. 13 is a graph of accuracy with respect to Elman learning times.

FIG. 14 is a graph of the X-axis position error predicted by the Elmanneural network after GNSS signals are blocked.

FIG. 15 is a graph of the Y-axis position error predicted by the Elmanneural network after GNSS signals are blocked.

FIG. 16 is a graph of the Z-axis position error predicted by the Elmanneural network after GNSS signals are blocked.

FIG. 17 is the Elman neural network assisting tight-integratednavigation system.

DETAILED DESCRIPTION

The specific embodiments of the present disclosure will be furtherdescribed below with reference to the drawings.

In order that the integrated navigation system can continue to providenavigation data when the GNSS signals are momentarily unavailable, thepresent disclosure provides a tight-integrated method assisted by anElman neural network when GNSS signals are blocked. The Elman neuralnetwork model is established by using appropriate hidden layer function.The tight-integrated navigational system may continue to work in thetight-integrated navigational mode by using the Elman neural networkmodel when the GNSS signals are blocked.

The specific steps are as follows:

Step 1: Establishing an Elman neural network model and selecting ahidden layer transfer function of the Elman neural network.

Step 2: Designing an Elman learning algorithm.

Step 3: Establishing a tight-integrated Kalman filter mathematicalmodel.

Step 4: Bringing the input and output of the tight-integrated Kalmanfilter mathematical model established in Step 3 into the Elman learningalgorithm designed in Step 2 to train the Elman neural network model.After the training is completed, the inertial navigation positioninformation is input to the neural network when the GNSS signals areblocked, so as to complete the tight-integrated algorithm assisted byElman neural network after obtaining the output of neural network.

The details of Step 1 is as follows:

FIG. 1 shows an Elman neural network structure designed in the presentdisclosure. The Elman neural network is a feedback neural network, andmainly comprises an input layer, a hidden layer, a connection layer andan output layer. The connection layer is used to connect the output andinput of the hidden layer, and memorizes and saves the output of thehidden layer at the previous time. The output of the hidden layer at theprevious time is used as the input of the hidden layer at the currenttime with a new input, and the connection layer functions as afirst-order delay operator. The network will be sensitive to historicaldata by the delay operator of the connection layer, and the capacity ofprocessing dynamic information by the system is improved. The Elmanneural network has dynamic memory capabilities because of the connectionlayer, so that the Elman neural network may be learned with respect tosystems having time-varying characteristics.

The mathematical model of the Elman neural network can be expressed asfollows:

xh(k)=f(W1P(k)+W3×(k))   (1)

xc(k)=αxh(k−1)   (2)

y(k)=g(W2×(k))   (3)

The vector P(k) represents an input vector of the Elman neural networkat time k, xh(k) represents an output vector of the hidden layer neuronat time k, x(k) represents an input vector of the Elman neural networkderived from the output of the hidden layer at time k, x_(c)(k)represents an output vector of the connection layer at time k, y(k)represents the output vector of the entire network output layer at timek, W 1, W2 and W3 are respectively the connection weight matrix betweenthe input layer and the hidden layer, between the hidden layer and theoutput layer, and between the connection layer and the hidden layer,f(⋅) and g(⋅) are the transfer functions of the hidden layer and theoutput layer respectively, and a is the connection feedback gain factor.

The transfer function is mainly used to limit the output of the neuronand keep the output value of the neuron within a predetermined range,and thus the transfer function may also be called as a squashingfunction. There are many types of transfer functions that can be used inneural networks, such as the S-type logarithmic functions, S-typetangent functions, and linear functions as shown in FIGS. 2 to 4. It canbe found from the figures that the input values of the three transferfunctions can be the values of any range, but the difference among threetransfer functions is the different range of the output amplitudecompression. Generally, the transfer function may be chosen according tothe needs of the application. In the disclosure, the input of the neuralnetwork is a position coordinate information calculated by the inertialnavigation, and the output is a position information compensated by theGNSS signals. Therefore, the input and output data may be positive ornegative. After normalizing the original data, the coordinate componentsare distributed in the range of [−1, 1], so the output of the hiddenlayer neuron must also be in range of [−1, 1]. The S-tangent functionmay be selected as the transfer function of the hidden layer neuron inthe disclosure.

The details of Step 2 are as follows:

The main calculation process of the Elman neural network is divided tocomprise the forward propagation of the working signal and the backwardpropagation of the error. The calculation of the forward propagation ofthe working signal is in consistent with the mathematical model of theElman neural network, and thus, the signal y(k) of the network outputmay be calculated. The back propagation of the error is specifically asfollows: that the actual output of the network is y(k) at time k isassumed, and the expected output response of the network is yd(k), thenthe error of the network is as follows:

E _(k)=½(y _(d)(k)−y(k))²   (4)

The partial derivative of the error function with respect to the weightbetween different layers such as the hidden layer and the output layeris obtained, respectively, the partial derivative of the error functionEk with respect to the connection weight matrix W2 from the hidden layerto the output layer can be obtained as follows:

$\begin{matrix}{\frac{\partial E}{\partial w_{ij}^{2}} = {{{- \left( {{y_{d,i}(k)} - {y(k)}} \right)}\frac{\partial{y_{i}(k)}}{\partial w_{ij}^{2}}} = {{- \left( {{y_{d,i}(k)} - {y(k)}} \right)}{g(\bullet)}{x_{j}(k)}}}} & (5)\end{matrix}$

wherein, i represents the i-th hidden layer neuron, which is the i-throw of the weight matrix W2, and j represents the j-th output layerneuron, which is the j-th column of the weight matrix W2.

Assuming δ_(i) ⁰=(y _(d,i)(k)−y(k))g(⋅), then:

$\begin{matrix}{{\frac{\partial E}{\partial w_{ij}^{2}} = {{- \delta_{i}^{0}}{x_{j}(k)}}};} & (6)\end{matrix}$

The partial derivative of Ek with respect to the connection weight W1from the input layer to the hidden layer can be obtained as follows:

$\begin{matrix}{\frac{\partial E}{\partial w_{ij}^{1}} = {{\frac{\partial E}{\partial{x_{j}(k)}}\frac{\partial{x_{j}(k)}}{\partial w_{ij}^{1}}} = {\sum{\left( {{- \delta_{i}^{0}}w_{ij}^{2}} \right){f_{j}^{\prime}(\bullet)}{P\left( {k - 1} \right)}}}}} & (7)\end{matrix}$

Assuming

${\delta_{j}^{h} = {\sum\limits_{i = 1}^{m}{\left( {{- \delta_{i}^{0}}w_{ij}^{2}} \right){f_{j}^{\prime}(\bullet)}}}},$

then:

$\begin{matrix}{\frac{\partial E}{\partial w_{ij}^{1}} = {{- \delta_{i}^{h}}{P\left( {k - 1} \right)}}} & (8)\end{matrix}$

Similarly, the partial derivative of Ek with respect to the connectionweight W3 from the connection layer to the hidden layer can be obtainedas follows:

$\begin{matrix}{\frac{\partial E}{\partial w_{ij}^{3}} = {{\sum{\left( {{- \delta_{i}^{0}}w_{ij}^{2}} \right)\frac{\partial{x_{j}(k)}}{\partial w_{ij}^{3}}}} = {{f_{j}^{\prime}{x_{c,l}(k)}} = {{{f_{j}^{\prime}(\bullet)}{x_{i}\left( {k - 1} \right)}} + {\alpha \; {f_{j}^{\prime}(\bullet)}{x_{c,l}(k)}}}}}} & (9)\end{matrix}$

The 1 is the 1-th neuron of the connection layer.

Using

${{\Delta \; w} = {- \frac{\partial E}{\partial w}}},$

the updated values for each weight may be obtained as follows:

$\begin{matrix}{{\Delta \; w_{ij}^{2}} = {\eta \; \delta_{i}^{0}{x_{j}(k)}}} & (10) \\{{\Delta \; w_{j}^{1}} = {\eta \; \delta_{i}{P\left( {k - 1} \right)}}} & (11) \\{{\Delta \; w_{ij}^{3}} = {\eta {\sum{\left( {\delta_{i}^{0}w_{ij}^{2}} \right)\frac{\partial{x_{j}(k)}}{\partial w_{jl}^{3}}\delta_{i}^{0}{x_{j}(k)}}}}} & (12)\end{matrix}$

Wherein,

δ_(i) ⁰=(y _(d,i)(k)−y(k))g _(i)(⋅)   (13)

δ_(j) ^(h)=Σ(δ_(i) ⁰ w _(ij) ²)f′ _(j)(⋅)   (14)

The details of Step 3 are as follows:

The Elman network structure is established, and then the Kalman filterin the tight-integrated navigation of INS and GPS is established, so asto use the position information before and after filtering as the inputand output of the neural network to train the neural network. The Kalmanfilter equation of the tight integration is established according to theerror equations of INS and GPS in the tight integrated navigation. The15-dimensional system state variables selected are as follows:

X=[δposδVδφε∇b_(clk)d_(clk)]  (15)

Wherein, δpos is the three position errors of the ECEF coordinatesystem, δV is the velocity error in the ENU(east north and up)coordinate system, δφ is the three posture errors of the inertialnavigation system, c is the three posture angle errors, ∇ is theacceleration zero-bias in three directions, bclk is the clock error, anddclk is the clock drift.

An external observation is obtained by the difference Z between thepseudo-range information and pseudo-range rate information obtained bythe inertial navigation system and the measurement information of thepseudo-range and pseudo-range rate of each GNSS satellite, the systemmeasurement equation is as follows:

$\begin{matrix}{Z = {\begin{bmatrix}Z_{\rho} \\Z_{\overset{.}{\rho}}\end{bmatrix} = {{HX} + V}}} & (16)\end{matrix}$

Wherein, H is the observation matrix, V is the observation noise, ρ isthe pseudo-range, and {dot over (P)} is the pseudo-range rate.

The integrated navigation system of inertial navigation and GNSS is anonlinear system. If the error is small, the inertial navigation postureerror is generally obtained by the state equation of linear error.However, when the inertial equipment accuracy is poor or the inertialnavigation system angle error is too large, non-linear factors in thenavigation system cannot be ignored, and the inertial navigation postureerror may be obtained by nonlinear filtering algorithm. The EKF(Extended Kalman Filter) is used to obtain the inertial navigationposture error.

The one-step prediction status:

Xk,k−b 1 =φk,k−1Xk−1   (17)

The status estimation:

Xk=Xk,k−1+Kk[Zk−hk(Xk,k−1)]  (18)

The one-step prediction error variance matrix:

P _(k,k−1)=ϕ_(k,k−1) P _(k−1)ϕ_(k,k−1) ^(T) +Q _(k−1)   (19)

The filter gain matrix:

k _(k) =P _(k,k . . . 1) H _(k) ^(T)(H _(k) P _(k,k . . . 1) H _(k) ^(T)+R _(K))⁻¹   (20)

Estimation error variance matrix:

Pk=(I−KkHK)Pk,k−1   (21)

Wherein, Φ is an error status transfer matrix, K is a Kalman gainmatrix, P is an error covariance matrix, and R is a noise covariancematrix.

The corrected position information X in the three directions iscalculated by the aforementioned Kalman filter, and the differencebetween the positions before and after the correction is brought intothe established Elman neural network as a output of neural networkduring the neural network training.

The details of Step 4 are as follows:

During network training, the number of input neurons and output neuronsof the network is the number of position parameters in three directionsin the ECEF coordinate system, that is, m is 3. The number I of neuronsin the hidden layer is 3. The input of the network is the positioninformation {circumflex over (x)}_(k) output by the inertial navigationof the integrated navigation system. The target output of the network isthe compensation inertial navigation position ΔE after the filtering ofthe integrated system. The input samples and output samples are broughtinto the y(k) and yd (k) of the Elman neural network established in theStep 2 to train the neural network, and the output x _(k) corrected byneural network is obtained after the training is completed.

Wherein,

ΔE=X _(k) −{circumflex over (X)} _(k)   (22)

The data of ΔE are saved in the Elman neural network model, and thus,the error of the inertial navigation may be corrected by retrieving theerror data ΔE at the corresponding sampling time.

The position X _(k) in the three directions in the ECEF coordinatesystem should be compensated in order to make a prediction, and thus:

X _(k) {circumflex over (X)} _(k) +ΔE   (23)

The status prediction estimation in the integrated navigation iscorrected in real time according to the trained network, and whencorrecting, the status variable {circumflex over (x)}_(k) of the EKFfilter of the integrated system is replaced by the X _(k), The specificmethod is shown in FIG. 5.

When the GNSS signals are available, the neural network works in thetraining mode, and the three-dimensional position information output bythe inertial navigation system is used as the input sample for trainingthe network. The compensation value of the inertial navigation erroroutput after the fusion of the Kalman filter is used as the expectedoutput samples for the training the network. When the error between theactual output and the expected output is more than the predeterminedthreshold (10-2 is set to meet the navigation error requirements in thepresent disclosures), the weight information is updated by the networkweight update algorithm in Step 2 until a set of optimal weights isobtained so that the error between the actual output of the network andthe expected output is less than the predetermined threshold.

The prediction process of the neural network is shown in FIG. 6. Whenthe GNSS signals are blocked, the neural network will work in theprediction mode. Similarly, the navigation position information outputby the inertial navigation system is used as the input of the network,and the error of the inertial navigation system is predicted by thetrained neural network model, and is used to correct the navigationoutput of the inertial navigation to provide the corrected navigationinformation for the mobile carrier.

In order to verify the reliability of the algorithm in practicalapplications, an experiment was carried out. The practical applicationvalue of the algorithm is verified by analyzing the error of GNSS in thecase of signal blocking and the error of integrated navigation under themachine learning of the present disclosure.

The embodiments of the present disclosure is described as follows:

In order to verify the effect of the random error suppression technologyof the dual-axis rotating inertial navigation system based on externalhorizontal damping proposed in this disclosure, the GNSS module ublox6,the inertial navigation module HWT901 and the core board STM32F4 ischosen for completing the experiment.

The ublox6 receiver connects to the HWT901B module packaged by ViterIntelligence Corporation with a gyroscope, a magnetometer and anaccelerometer, the data of the two modules are sent to STM32F4 throughthe serial port and finally sent to the computer for processing toensure the time alignment of the two sensors. The specific indexes ofthe HWT901B module are shown in Table 1:

TABLE 1 the specific indexes table of the HWT901B module Title gyroscopeaccelerometer Constant drift ±3°/s ±25 mg Random Walk 0.007°/s/√{squareroot over (Hz)} 180 ug/√{square root over (Hz)}

A total of 500s data is collected for the experiment, and 100s dataafter shielding is collected for the experiment so as to simulate thesignal blocking situation, the position error before blocking is shownin FIGS. 7-9.

The error after blocking is shown in FIGS. 10-12.

It can be found that the satellite signal is blocked at 400s from thefigure, the device itself has low accuracy because the inertialnavigation device is low-cost, and thus, the navigation system that onlyrelies on the inertial navigation disperses rapidly, and the system iscompletely unable to positioning due to the increased error. As acontrast, the results obtained by the Elman neural network algorithm areshown in FIG. 13.

It can be found that the accuracy has reached 10-2 which can fully meetthe prediction needs when the number of learning reaches 100 times. Thelearning times and the reached accuracy may be variable in the learningalgorithm in the present disclosures. Even if the training times isreduced, such as 50 times, and the accuracy can reach 10-1. When theoutput errors of all samples meet the allowable range, the networktraining ends. And the trained neural network may be used to makepredictions. The predicted position error results are shown in FIGS.14-16.

It can be found that the position error of the three directions based onElman prediction is close to the previous time when the GNSS signals areblocked. Although there is some divergence as time goes by, the positionerror corrected by the error prediction is still acceptable. That is,the inertial navigation information compensated by Elman does notdiverge rapidly like the situation shown in the FIG. 11-13, and thenavigation accuracy of the ship can be met by the algorithm in thepresent disclosure.

The present disclosure further provide an Elman neural network assistingtight-integrated navigation system, comprising: a GNSS receiver forreceiving GNSS signals, an INS receiver for receiving INS signals, aKalman filter for executing a filtering process of received signals, anda processor operable to establish an Elman neural network model andselecting a hidden layer transfer function of the Elman neural network,design an Elman learning algorithm, and establish a tight-integratedKalman filter mathematical model.

When the GNSS signals are available, the Elman neural network works in atraining mode, a three-dimensional position information outputted by theINS receiver is used as input samples for training the Elman neuralnetwork designed by the processer; a compensation value of an inertialnavigation error output after a fusion of the Kalman filter is used asexpected output samples for training the Elman neural network, and theinput samples and the expected output samples are brought into the Elmanneural network established for training the Elman neural network; whenerrors between actual outputs of the Elman neural network and theexpected output samples are more than a predetermined threshold, anupdated value of a network weight is obtained by cyclically using theElman neural network until the errors between the actual outputs of theElman neural and the expected outputs are less than the predeterminedthreshold, and when the GNSS signals are blocked, the Elman neuralnetwork works in a prediction mode; a navigation position informationoutput by the INS receiver is used as the input of the trained neuralnetwork, an error of the inertial navigation system is predicted by thetrained neural network, and a corrected navigation information isobtained by correcting the navigation output of the INS receiver by theerror predicted by the Elman neural network.

The Elman neural network assisting tight-integrated navigation systemwill be described with reference to FIG. 17, which depicts an exemplarysystem.

As shown in FIG. 17, the system 10 may include the GNSS receiver 110,INS receiver 120 and the processing system 200.

Referring to FIGS. 5 and 17, the GNSS receiver 110 may receive the GNSSsignals, and provide the pseudo-range and the pseudo-range rate to theprocessing system 200. The INS receiver 120 may receive the INS signalsand provide the position information, velocity information, postureinformation and the error to the processing system 200.

The processing system 200 may include the processor 210, theComputer-Readable Medium/Memory 220 and the Kalman filer 230. In oneexample embodiment, the Kalman processor 230 may be implemented as asoftware executable by the processor 210.

The apparatus may include additional components that perform thealgorithm of the present disclosure. Each step of the algorithm may beperformed by a component and the apparatus may include one or more ofthose components. The components may be one or more hardware componentsspecifically configured to carry out the processes/algorithm,implemented by a processor configured to perform the statedprocesses/algorithm, stored within a computer-readable medium 220 forimplementation by a processor, or some combination thereof.

The processing system 200 may be implemented with a bus architecture,represented generally by the bus 240. The bus 240 may include any numberof interconnecting buses and bridges depending on the specificapplication of the processing system 200 and the overall designconstraints. The bus 200 links together various circuits including oneor more processors and/or hardware components, represented by theprocessor 210, the Computer-Readable Medium/Memory 220 and the Kalmanfiler 230. The bus 200 may also link various other circuits such astiming sources, peripherals, voltage regulators, and power managementcircuits, which are well known in the art, and therefore, will not bedescribed any further.

The processing system 200 may be coupled to the GNSS receiver 110 andthe INS receiver 120. The GNSS receiver 110 and the INS receiver 120 arecoupled to one or more antennas. The GNSS receiver 110 and the INSreceiver 120 provide a means for communicating with various otherapparatus over a transmission medium. The GNSS receiver 110 and the INSreceiver 120 receive signals from the one or more antennas, extractsinformation from the received signal, and provides the extractedinformation to the processing system 200, specifically the processor 210and the Kalman filer 230. The processing system 200 includes a processor210 coupled to a computer-readable medium/memory 220. The processor 210is responsible for general processing, including the execution ofsoftware stored on the computer-readable medium/memory 210. Thesoftware, when executed by the processor 210, causes the processingsystem 200 to perform the various functions described supra for anyparticular apparatus. The computer-readable medium/memory 220 may alsobe used for storing data that is manipulated by the processor 210 whenexecuting software.

While certain embodiments have been described, it will be understoodthat various modifications can be made without departing from the scopeof the present disclosure. Thus, it will be apparent to those ofordinary skill in the art that the present disclosure is not limited toany of the embodiments described herein, but rather has a coveragedefined only by the appended claims and their equivalents.

1. An Elman neural network assisting tight-integrated navigation methodwithout GNSS signals, comprising: step 1: establishing an Elman neuralnetwork model and selecting a hidden layer transfer function of theElman neural network, step 2: designing an Elman learning algorithm,step 3: establishing a tight-integrated Kalman filter mathematicalmodel, step 4: when the GNSS signals are available, the neural networkworks in a training mode, a three-dimensional position informationoutput by an inertial navigation system is used as input samples fortraining the neural network designed in the step 2; a compensation valueof an inertial navigation error output after a fusion of the Kalmanfilter established in step 3 is used as expected output samples fortraining the network, and the input samples and the expected outputsamples are brought into the Elman neural network established in thestep 2 for training the Elman neural network; when errors between actualoutputs of the Elman neural network and the expected output samples aremore than a predetermined threshold, an updated value of a networkweight is obtained by cyclically using the Elman neural networkalgorithm designed in step 2 until the errors between the actual outputsof the network and the expected outputs are less than the predeterminedthreshold, and step 5: when the GNSS signals are blocked, the neuralnetwork works in a prediction mode; a navigation position informationoutput by the inertial navigation system is used as the input of thenetwork trained by the step 4, an error of the inertial navigationsystem is predicted by the neural network model trained by the step 4,and a corrected navigation information is obtained by correcting thenavigation output of the inertial navigation system by the errorpredicted by the neural network model.
 2. The method as claimed in claim1, wherein, the Elman neural network comprises an input layer, a hiddenlayer, a connection layer and an output layer, the mathematical model ofthe Elman neural network is expressed as follows:x _(h)(k)=f(W ₁ P(k)+W ₃×(k));x _(c)(k)=αx _(h)(k−1);y(k)=g(W ₂×(k)); wherein, P(k) represents an input vector of the Elmanneural network at time k, x_(h)(k) represents an output vector of thehidden layer neuron at time k, x(k) represents an input vector of theElman neural network derived from the output of the hidden layer at timek, x_(c)(k) represents an output vector of the connection layer at timek, y(k) represents the output vector of the entire network output layerat time k, W₁, W₂ and W₃ are respectively connection weight matrixesbetween the input layer and the hidden layer, between the hidden layerand the output layer, and between the connection layer and the hiddenlayer, f(⋅) and g(⋅) are respectively transfer functions of the hiddenlayer and the output layer, and a is a connection feedback gain factor.3. The method as claimed in claim 1, wherein, an S-tangent function isselected as the transfer function of the hidden layer of Elman neuralnetwork.
 4. The method as claimed in claim 1, wherein, the step 2comprises, a calculation process of the Elman neural network is dividedto comprise a forward propagation of a working signal and a backwardpropagation of the error; the calculation of the forward propagation ofthe working signal is in consistent with the mathematical model of theElman neural network, and the signal y(k) of the network output iscalculated; the back propagation of the error is as follows: that theactual output of the network is y(k) at time k is assumed, and theexpected output response of the network is y_(d)(k), then the error ofthe network is as follows:E _(k)=½(y _(d)(k))−y(k))² partial derivatives of the error functionwith respect to the connection weights between different layers areobtained, respectively; the partial derivative of the error function Ekwith respect to the connection weight matrix W₂ from the hidden layer tothe output layer is obtained as follows:$\frac{\partial E}{\partial w_{ij}^{2}} = {{{- \left( {{y_{d,i}(k)} - {y(k)}} \right)}\frac{\partial{y_{i}(k)}}{\partial w_{ij}^{2}}} = {{- \left( {{y_{d,i}(k)} - {y(k)}} \right)}{g(\bullet)}{x_{j}(k)}}}$wherein, i represents an i-th hidden layer neuron, which is the i-th rowof the weight matrix W₂, and j represents a j-th output layer neuron,which is the j-th column of the weight matrix W₂; assuming δ_(i) ⁰=(y_(d,i)(k)−y(k))g(∩), then:$\frac{\partial E}{\partial w_{ij}^{2}} = {{- \delta_{i}^{0}}{x_{j}(k)}}$the partial derivative of Ek with respect to the connection weightmatrix W₁ from the input layer to the hidden layer is obtained asfollows:$\frac{\partial E}{\partial w_{ij}^{1}} = {{\frac{\partial E}{\partial{x_{j}(k)}}\frac{\partial{x_{j}(k)}}{\partial w_{ij}^{1}}} = {\sum{\left( {{- \delta_{i}^{0}}w_{ij}^{2}} \right){f_{j}^{\prime}(\bullet)}{P\left( {k - 1} \right)}}}}$assuming${\delta_{j}^{h} = {\sum\limits_{i = 1}^{m}{\left( {{- \delta_{i}^{0}}w_{ij}^{2}} \right){f_{j}^{\prime}(\bullet)}}}},$then:$\frac{\partial E}{\partial w_{ij}^{1}} = {{- \delta_{i}^{h}}{P\left( {k - 1} \right)}}$the partial derivative of Ek with respect to the connection weightmatrix W₃ from the connection layer to the hidden layer is obtained asfollows:$\frac{\partial E}{\partial w_{ij}^{3}} = {{\sum{\left( {{- \delta_{i}^{0}}w_{ij}^{2}} \right)\frac{\partial{x_{j}(k)}}{\partial w_{ij}^{3}}}} = {{f_{j}^{\prime}{x_{c,i}(k)}} = {{{f_{j}^{\prime}(\bullet)}{x_{i}\left( {k - 1} \right)}} + {\alpha \; {f_{j}^{\prime}(\bullet)}{x_{c,i}(k)}}}}}$wherein, l is the l-th neuron of the connection layer; using${{\Delta \; w} = {- \frac{\partial E}{\partial w}}},$ updated valuesfor each weight may be obtained as follows: $\begin{matrix}{{\Delta \; w_{ij}^{2}} = {\eta \; \delta_{i}^{0}{x_{j}(k)}}} \\{{\Delta \; w_{j}^{1}} = {\eta \; \delta_{i}{P\left( {k - 1} \right)}}} \\{{\Delta \; w_{ij}^{3}} = {\eta {\sum{\left( {\delta_{i}^{0}w_{ij}^{2}} \right)\frac{\partial{x_{j}(k)}}{\partial w_{jl}^{3}}\delta_{i}^{0}{x_{j}(k)}}}}}\end{matrix}$ wherein,δ_(i) ⁰=(y _(d,i)(k)−y(k))g _(i)(⋅)δ_(j) ^(h)=Σ(δ_(i) ⁰ w _(ij) ²)f′ _(j)(⋅)
 5. The method as claimed inclaim 1, wherein, the step 3 comprises, 15-dimensional system statevariables selected are as follows:X=[δposδVδφε∇b_(clk)d_(clk)] wherein, δpos is three position errors ofthe ECEF coordinate system, δV is a velocity error in the ENU coordinatesystem, δ is three posture errors of the inertial navigation system, εis three posture angle errors, ∇ is acceleration zero-biases in threedirections, b_(clk) is a clock error, and d_(clk) is a clock drift; anexternal observation is obtained by the difference Z between thepseudo-range information and pseudo-range rate information obtained bythe inertial navigation system and the measurement information of thepseudo-range and pseudo-range rate of each GNSS satellite, a systemmeasurement equation is as follows: $Z = {\begin{bmatrix}Z_{\rho} \\Z_{\overset{.}{\rho}}\end{bmatrix} = {{HX} + V}}$ wherein, H is an observation matrix, V isan observation noise, ρ is a pseudo-range, and {dot over (P)} is apseudo-range rate; a filtering calculation is performed by the EKF forthe integrated navigation, the detailed filtering calculation is asfollows: one-step prediction status:X_(k,k−1)=φ_(k,k−1)X_(k−1) a status estimation:X _(k) =X _(k,k−1) +K _(k) [Z _(k) −h _(k)(X _(k,k−1))] a one-stepprediction error variance matrix: P _(k,k−1)=ϕ_(k,k−1) P_(k−1)ϕ_(k,k,−1) ^(T) +Q _(k−1) a filter gain matrix:K _(k) =P _(k,k . . . 1) H _(k) ^(T)(H _(K) P _(k,k . . . 1) H _(k) ^(T)+R _(K))^(. . . 1) an estimation error variance matrix:Phd k=(I−K _(k) H _(K))P _(k,k−1) wherein, Φ is an error status transfermatrix, K is a Kalman gain matrix, P is an error covariance matrix, andR is a noise covariance matrix; the corrected position information X inthree directions is calculated by the aforementioned Kalman filter, andthe difference between the positions before and after the correction isbrought into the established Elman neural network as an output of neuralnetwork during the neural network training.
 6. The method as claimed inclaim 1, wherein, the step 4 comprises, during network training, thenumber of input neurons and output neurons of the network is the numberof position parameters in three directions in the ECEF coordinatesystem, m is 3; the number I of neurons in the hidden layer is 3; theinput of the network is the position information {circumflex over(x)}_(k) output by the inertial navigation of the integrated navigationsystem, the target output of the network is the compensation inertialnavigation position ΔE after filtering of the integrated system; theinput samples and output samples are brought into the y(k) and yd (k) ofthe Elman neural network established in the step 2 to train the neuralnetwork, and the output {umlaut over (x)}_(k) corrected by neuralnetwork is obtained after the training is completed, wherein, ΔE=X_(k)−{circumflex over (X)}_(k) the data of ΔE are saved in the Elmanneural network model, and the error of the inertial navigation iscorrected by retrieving the error data ΔE at the corresponding samplingtime; the position x _(k) in the three directions in the ECEF coordinatesystem is compensated in order to make a prediction,X _(k) ={circumflex over (X)} _(k) +ΔE the status prediction estimationin the integrated navigation is corrected in real time according to thetrained network, and when correcting, the status variable {circumflexover (X)}_(k) of the EKF filter of the integrated system is replaced bythe x _(k).
 7. An Elman neural network assisting tight-integratednavigation system, comprising: a GNSS receiver for receiving GNSSsignals, an INS receiver for receiving INS signals, a Kalman filter forexecuting a filtering process of received signals, and a processoroperable to establish an Elman neural network model and selecting ahidden layer transfer function of the Elman neural network, design anElman learning algorithm, and establish a tight-integrated Kalman filtermathematical model, wherein, when the GNSS signals are available, theElman neural network works in a training mode, a three-dimensionalposition information outputted by the INS receiver is used as inputsamples for training the Elman neural network designed by the processer;a compensation value of an inertial navigation error output after afusion of the Kalman filter is used as expected output samples fortraining the Elman neural network, and the input samples and theexpected output samples are brought into the Elman neural networkestablished for training the Elman neural network; when errors betweenactual outputs of the Elman neural network and the expected outputsamples are more than a predetermined threshold, an updated value of anetwork weight is obtained by cyclically using the Elman neural networkuntil the errors between the actual outputs of the Elman neural and theexpected outputs are less than the predetermined threshold, and when theGNSS signals are blocked, the Elman neural network works in a predictionmode; a navigation position information output by the INS receiver isused as the input of the trained neural network, an error of theinertial navigation system is predicted by the trained neural network,and a corrected navigation information is obtained by correcting thenavigation output of the INS receiver by the error predicted by theElman neural network.